Pub Date : 2012-01-01DOI: 10.1080/00411450.2012.671215
F. V. van Heerden
This article introduces a novel coarse-grained particle transport solver, designed specifically for streaming processor architectures. The coarse particles are transported using a Monte Carlo algorithm with a locally homogenized collision operator. Local errors introduced by the homogenization procedure and the use of (deterministic) quadratures, are described and analyzed. A brief description of how the simulation is mapped to the streaming processor (Graphics Processing Unit) is also given.
{"title":"A Coarse Grained Particle Transport Solver Designed Specifically for Graphics Processing Units","authors":"F. V. van Heerden","doi":"10.1080/00411450.2012.671215","DOIUrl":"https://doi.org/10.1080/00411450.2012.671215","url":null,"abstract":"This article introduces a novel coarse-grained particle transport solver, designed specifically for streaming processor architectures. The coarse particles are transported using a Monte Carlo algorithm with a locally homogenized collision operator. Local errors introduced by the homogenization procedure and the use of (deterministic) quadratures, are described and analyzed. A brief description of how the simulation is mapped to the streaming processor (Graphics Processing Unit) is also given.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"41 1","pages":"100 - 80"},"PeriodicalIF":0.0,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2012.671215","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909761","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-01-01DOI: 10.1080/00411450.2012.671219
P. Picca, R. Furfaro, B. Ganapol
The article presents a novel kinetic method for the solution of time-dependent source-driven linear transport problems. As will be discussed, the method is based on a multigeneration representation of linear Boltzmann equations and is derived from physically grounded considerations. The technique is said to be hybrid since it combines together collisionless transport solutions and factorization techniques. The methodology is tested on systems with different scattering properties and shows very promising performance both in terms of accuracy and computational times.
{"title":"Derivation of a Physically Based Hybrid Technique for the Solution of Source-Driven Time-Dependent Linear Boltzmann Equations","authors":"P. Picca, R. Furfaro, B. Ganapol","doi":"10.1080/00411450.2012.671219","DOIUrl":"https://doi.org/10.1080/00411450.2012.671219","url":null,"abstract":"The article presents a novel kinetic method for the solution of time-dependent source-driven linear transport problems. As will be discussed, the method is based on a multigeneration representation of linear Boltzmann equations and is derived from physically grounded considerations. The technique is said to be hybrid since it combines together collisionless transport solutions and factorization techniques. The methodology is tested on systems with different scattering properties and shows very promising performance both in terms of accuracy and computational times.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"41 1","pages":"23 - 39"},"PeriodicalIF":0.0,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2012.671219","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909843","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-01-01DOI: 10.1080/00411450.2012.671214
J. Cartier, M. Peybernes
In this article we deal with a mixed and hybrid finite element method slab geometry discretization of the transport equation arising from the new variational formulation introduced in Cartier and Peybernes (2011). The aim of this study is to construct such a discretization by preserving the diffusion limit in the entire diffusive region, close to the boundaries, and for internal interface problems.
{"title":"Improved Mixed and Hybrid Discretization of the Transport Equation in Slab Geometry","authors":"J. Cartier, M. Peybernes","doi":"10.1080/00411450.2012.671214","DOIUrl":"https://doi.org/10.1080/00411450.2012.671214","url":null,"abstract":"In this article we deal with a mixed and hybrid finite element method slab geometry discretization of the transport equation arising from the new variational formulation introduced in Cartier and Peybernes (2011). The aim of this study is to construct such a discretization by preserving the diffusion limit in the entire diffusive region, close to the boundaries, and for internal interface problems.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"41 1","pages":"40 - 52"},"PeriodicalIF":0.0,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2012.671214","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-01-01DOI: 10.1080/00411450.2012.726172
T. Palmer
{"title":"The 22nd International Conference on Transport Theory, Portland, Oregon, September 11–15, 2011","authors":"T. Palmer","doi":"10.1080/00411450.2012.726172","DOIUrl":"https://doi.org/10.1080/00411450.2012.726172","url":null,"abstract":"","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"41 1","pages":"i - iii"},"PeriodicalIF":0.0,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2012.726172","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909735","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-01-01DOI: 10.1080/00411450.2012.671206
M. Asadzadeh, Tobias Gebäck
This work is the first part in a series of two articles, where the objective is to construct, analyze, and implement realistic particle transport models relevant in applications in radiation cancer therapy. Here we use spherical harmonics and derive an energy-dependent model problem for the transport equation. Then we show stability and derive optimal convergence rates for semidiscrete (discretization in energy) finite element approximations of this model problem. The fully discrete problem that also considers the study of finite element discretizations in radial and spatial domains as well is the subject of a forthcoming article.
{"title":"Spherical Harmonics and a Semidiscrete Finite Element Approximation for the Transport Equation","authors":"M. Asadzadeh, Tobias Gebäck","doi":"10.1080/00411450.2012.671206","DOIUrl":"https://doi.org/10.1080/00411450.2012.671206","url":null,"abstract":"This work is the first part in a series of two articles, where the objective is to construct, analyze, and implement realistic particle transport models relevant in applications in radiation cancer therapy. Here we use spherical harmonics and derive an energy-dependent model problem for the transport equation. Then we show stability and derive optimal convergence rates for semidiscrete (discretization in energy) finite element approximations of this model problem. The fully discrete problem that also considers the study of finite element discretizations in radial and spatial domains as well is the subject of a forthcoming article.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"41 1","pages":"53 - 70"},"PeriodicalIF":0.0,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2012.671206","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-01-01DOI: 10.1080/00411450.2012.672359
Y. Bang, Congjiang Wang, H. Abdel-Khalik
Introduced here is an adjoint state-based method for model reduction, which provides a single solution to two classes of reduction methods that are currently in the literature. The first class, which represents the main subject of this manuscript, is concerned with linear time invariant problems where one is interested in calculating linear responses variations resulting from initial conditions perturbations. The other class focuses on perturbations introduced in the operator, which result in nonlinear responses variations. Unlike existing adjoint-based methods where an adjoint function is calculated based on a given response, the state-based method employs the state variations to set up a number of adjoint problems, each corresponding to a pseudoresponse. This manuscript extends the applicability of state-based method to generate reduced order models for linear time invariant problems. Previous developments focusing on operator perturbations are reviewed briefly to highlight the common features of the state-based algorithm as applied to these two different classes of problems. Similar to previous developments, the state-based reduction is shown to set an upper-bound on the maximum discrepancy between the reduced and original model predictions. The methodology is applied and compared to other state-of-the-art methods employing several nuclear reactor diffusion and transport models.
{"title":"State-Based Adjoint Method for Reduced Order Modeling","authors":"Y. Bang, Congjiang Wang, H. Abdel-Khalik","doi":"10.1080/00411450.2012.672359","DOIUrl":"https://doi.org/10.1080/00411450.2012.672359","url":null,"abstract":"Introduced here is an adjoint state-based method for model reduction, which provides a single solution to two classes of reduction methods that are currently in the literature. The first class, which represents the main subject of this manuscript, is concerned with linear time invariant problems where one is interested in calculating linear responses variations resulting from initial conditions perturbations. The other class focuses on perturbations introduced in the operator, which result in nonlinear responses variations. Unlike existing adjoint-based methods where an adjoint function is calculated based on a given response, the state-based method employs the state variations to set up a number of adjoint problems, each corresponding to a pseudoresponse. This manuscript extends the applicability of state-based method to generate reduced order models for linear time invariant problems. Previous developments focusing on operator perturbations are reviewed briefly to highlight the common features of the state-based algorithm as applied to these two different classes of problems. Similar to previous developments, the state-based reduction is shown to set an upper-bound on the maximum discrepancy between the reduced and original model predictions. The methodology is applied and compared to other state-of-the-art methods employing several nuclear reactor diffusion and transport models.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"70 1","pages":"101 - 132"},"PeriodicalIF":0.0,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2012.672359","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58910026","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-01-01DOI: 10.1080/00411450.2012.671216
A. Mekkaoui, Y. Marandet, H. Capes, D. Reiter, L. Godbert-Mouret, M. Koubiti, J. Rosato, R. Stamm
Neutral particles (atoms, molecules) play an important role in thermonuclear fusion magnetic confinement devices. At the very edge of the plasma, close to the wall, density fluctuations with amplitude comparable to the mean density have been reported. In this work, we analyze the effect of these fluctuations on the transport of neutral particles, using a multivariate Gamma model to describe the spatial correlations of fluctuations. Analytical results are obtained in 1D for the average neutral particle density in the presence of scattering.
{"title":"Particle Transport in Stochastic Media With Multivariate Gamma Statistics: Analytical Results With Application to Atoms in Tokamaks","authors":"A. Mekkaoui, Y. Marandet, H. Capes, D. Reiter, L. Godbert-Mouret, M. Koubiti, J. Rosato, R. Stamm","doi":"10.1080/00411450.2012.671216","DOIUrl":"https://doi.org/10.1080/00411450.2012.671216","url":null,"abstract":"Neutral particles (atoms, molecules) play an important role in thermonuclear fusion magnetic confinement devices. At the very edge of the plasma, close to the wall, density fluctuations with amplitude comparable to the mean density have been reported. In this work, we analyze the effect of these fluctuations on the transport of neutral particles, using a multivariate Gamma model to describe the spatial correlations of fluctuations. Analytical results are obtained in 1D for the average neutral particle density in the presence of scattering.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"41 1","pages":"71 - 79"},"PeriodicalIF":0.0,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2012.671216","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-01-01DOI: 10.1080/00411450.2012.672944
Bruno Turcksin, J. Ragusa, J. Morel
It is well known that the diffusion synthetic acceleration (DSA) methods for the Sn equations become ineffective in the Fokker-Planck forward-peaked scattering limit. In response to this deficiency, Morel and Manteuffel (1991) developed an angular multigrid method for the 1-D Sn equations. This method is very effective, costing roughly twice as much as DSA per source iteration, and yielding a maximum spectral radius of approximately 0.6 in the Fokker-Planck limit. Pautz, Adams, and Morel (PAM) (1999) later generalized the angular multigrid to 2-D, but it was found that the method was unstable with sufficiently forward-peaked mappings between the angular grids. The method was stabilized via a filtering technique based on diffusion operators, but this filtering also degraded the effectiveness of the overall scheme. The spectral radius was not bounded away from unity in the Fokker-Planck limit, although the method remained more effective than DSA. The purpose of this article is to recast the multidimensional PAM angular multigrid method without the filtering as an Sn preconditioner and use it in conjunction with the Generalized Minimal RESidual (GMRES) Krylov method. The approach ensures stability and our computational results demonstrate that it is also significantly more efficient than an analogous DSA-preconditioned Krylov method.
众所周知，Sn方程的扩散合成加速(DSA)方法在Fokker-Planck前峰散射极限下是无效的。针对这一缺陷，Morel和Manteuffel(1991)开发了一维Sn方程的角多重网格方法。这种方法非常有效，每次源迭代的成本大约是DSA的两倍，并且在Fokker-Planck极限下产生的最大光谱半径约为0.6。Pautz, Adams, and Morel (PAM)(1999)后来将角多重网格推广到二维，但发现该方法在角网格之间有足够的前峰映射时是不稳定的。该方法通过基于扩散算子的滤波技术来稳定，但这种滤波也降低了整体方案的有效性。在Fokker-Planck极限下，谱半径没有偏离单位，尽管该方法仍然比DSA更有效。本文的目的是将不带滤波的多维PAM角多重网格方法重新定义为Sn预条件，并将其与广义最小残差(GMRES) Krylov方法结合使用。该方法保证了稳定性，并且我们的计算结果表明，它也明显比类似的dsa预处理Krylov方法更有效。
{"title":"Angular Multigrid Preconditioner for Krylov-Based Solution Techniques Applied to the Sn Equations with Highly Forward-Peaked Scattering","authors":"Bruno Turcksin, J. Ragusa, J. Morel","doi":"10.1080/00411450.2012.672944","DOIUrl":"https://doi.org/10.1080/00411450.2012.672944","url":null,"abstract":"It is well known that the diffusion synthetic acceleration (DSA) methods for the Sn equations become ineffective in the Fokker-Planck forward-peaked scattering limit. In response to this deficiency, Morel and Manteuffel (1991) developed an angular multigrid method for the 1-D Sn equations. This method is very effective, costing roughly twice as much as DSA per source iteration, and yielding a maximum spectral radius of approximately 0.6 in the Fokker-Planck limit. Pautz, Adams, and Morel (PAM) (1999) later generalized the angular multigrid to 2-D, but it was found that the method was unstable with sufficiently forward-peaked mappings between the angular grids. The method was stabilized via a filtering technique based on diffusion operators, but this filtering also degraded the effectiveness of the overall scheme. The spectral radius was not bounded away from unity in the Fokker-Planck limit, although the method remained more effective than DSA. The purpose of this article is to recast the multidimensional PAM angular multigrid method without the filtering as an Sn preconditioner and use it in conjunction with the Generalized Minimal RESidual (GMRES) Krylov method. The approach ensures stability and our computational results demonstrate that it is also significantly more efficient than an analogous DSA-preconditioned Krylov method.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"41 1","pages":"1 - 22"},"PeriodicalIF":0.0,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2012.672944","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58910052","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-01-01DOI: 10.1080/00411450.2012.671212
A. Seubert, A. Sureda, Janis Lapins, J. Bader, E. Laurien
This article describes the 3D discrete ordinates–based coupled code system TORT-TD/ATTICA3D that aims at steady state and transient analyses of pebble-bed high-temperature gas cooled reactors. In view of increasing computing power, the application of time-dependent neutron transport methods becomes feasible for best estimate evaluations of safety margins. The calculation capabilities of TORT-TD/ATTICA3D are presented along with the coupling approach, with focus on the time-dependent neutron transport features of TORT-TD. Results obtained for the OECD/NEA/NSC PBMR-400 benchmark demonstrate the transient capabilities of TORT-TD/ATTICA3D.
{"title":"The Transient 3-D Transport Coupled Code TORT-TD/ATTICA3D for High-Fidelity Pebble-Bed HTGR Analyses","authors":"A. Seubert, A. Sureda, Janis Lapins, J. Bader, E. Laurien","doi":"10.1080/00411450.2012.671212","DOIUrl":"https://doi.org/10.1080/00411450.2012.671212","url":null,"abstract":"This article describes the 3D discrete ordinates–based coupled code system TORT-TD/ATTICA3D that aims at steady state and transient analyses of pebble-bed high-temperature gas cooled reactors. In view of increasing computing power, the application of time-dependent neutron transport methods becomes feasible for best estimate evaluations of safety margins. The calculation capabilities of TORT-TD/ATTICA3D are presented along with the coupling approach, with focus on the time-dependent neutron transport features of TORT-TD. Results obtained for the OECD/NEA/NSC PBMR-400 benchmark demonstrate the transient capabilities of TORT-TD/ATTICA3D.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"41 1","pages":"133 - 152"},"PeriodicalIF":0.0,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2012.671212","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909690","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2011-12-02DOI: 10.1080/00411450.2011.651031
J. Calvo
The purpose of this article is to refine and complement the results obtained in Calogero et al. (2010) on the dispersive behavior for solutions to the Vlasov-Poisson system in the stellar dynamics case. I will focus mainly on solutions that have zero energy in the center of mass system.
{"title":"On Dispersion Rates for Solutions to the Vlasov-Poisson System","authors":"J. Calvo","doi":"10.1080/00411450.2011.651031","DOIUrl":"https://doi.org/10.1080/00411450.2011.651031","url":null,"abstract":"The purpose of this article is to refine and complement the results obtained in Calogero et al. (2010) on the dispersive behavior for solutions to the Vlasov-Poisson system in the stellar dynamics case. I will focus mainly on solutions that have zero energy in the center of mass system.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"40 1","pages":"312 - 330"},"PeriodicalIF":0.0,"publicationDate":"2011-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2011.651031","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909465","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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